Exam 15: Nonparametric Statistics

The runs test is appropriate for which type of data?

With the Wilcoxon sign-ranked test, what is done in the case of equal values?

A manufacturer has three machine lines (Red, White, and Blue) that produce the same product.The product can be scrutinized for eccentricity based on an evaluation process that returns a raw score indicating the product's departure from the standard (a higher score indicates more eccentricity).Six products are chosen at random from each line. ​ ​ Conduct a Kruskal-Wallis test to see if the production lines appear to differ.Use a approximation.Select the appropriate critical value (CV), test statistic (TS), and decision.(Use α = 0.05.)

A manufacturer of ballpoint pens wishes to know if a machine designed to fill each individual pen with ink is operating properly.The median amount of ink should be 0.05 oz.Suppose 58 pens are randomly sampled from this particular machine, and none of the pens contains exactly 0.05 oz.Assuming the amount of ink in each pen is symmetrically distributed, conduct a Wilcoxon signed-rank test to see if the median amount of ink differs from 0.05 oz.The sum of positive differences (t+) from the sample is 502.Use a normal approximation and select the correct p-value and decision.(Use α = 0.05.)

When comparing the output of strawberries grown on plots using fertilizer A with that grown on otherwise identical plots using fertilizer B, making a general assessment of relative fertilizer effectiveness may well call for a:

The total number of words per page is recorded from a random sample of 17 pages printed using a standard font and from 20 pages using a new font.A Wilcoxon rank-sum test is performed, and the sum of the ranks of the standard font sample (sample 1) is 301 .Using a normal approximation, does the new font appear to increase the median number of words per page? Assume the number of words per page can be modeled as a continuous variable.Select the correct p-value and decision.(Use α = 0.05.)

With the Wilcoxon rank-sum test, what is done in the case of equal values?

Two variables have a Spearman's rank correlation coefficient of -0.9872.We can conclude from this that:

Calculate the Spearman's rank correlation coefficient for the following data: ​ ​

The smallest possible number of runs in any sample is:

Consider the following statements: ​ ​ Where The null hypothesis can be interpreted as:

In a Kruskal-Wallis test, the null hypothesis is always that:

If , then the value is subtracted from each observation in sample 1.This will:

In the Wilcoxon rank-sum test, the null hypothesis may be expressed as: ​ ​ If , then:

A normal approximation for the Wilcoxon rank-sum test is appropriate when:

Concerning the runs test, a normal approximation is appropriate when:

In the Wilcoxon signed-rank test, if two or more measurements have the same nonzero difference, then:

With the Kruskal-Wallis test, the data from all k samples are combined and each observation is assigned a rank.What is done in the case of equal values?

An athletic trainer is concerned that his athletes are not drinking enough water during games.He randomly samples 11 previous games with comparable temperature and humidity and records the amount of water consumed by the team in liters (shown in the table).Conduct a sign test to see if the median amount of water consumed exceeds 30 L.(Assume that the amount of water consumed per game is a continuous variable.) ​ Amount of Water Consumed per Game (in liters) Select the correct critical value (CV), test statistic (TS), and decision.(Use α = 0.10.)

Nonparametric tests can be appropriate for quantitative data when: